CN112116541B - Based on gradient l0Fuzzy image restoration method based on norms and total variation regularization constraint - Google Patents
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Abstract
The invention relates to a fuzzy image restoration method based on regularization constraint of gradient l 0 norms and total variation, which comprises the following steps: modeling the noise of the blurred image and the clear image and modeling a point spread function; introducing two regularization constraint coefficients, weighting and summing the three models, and constructing a fuzzy image restoration problem model; decomposing the model into optimal estimation problems with respect to sharp images and point spread functions; initializing a clear image and a point spread function estimated value; solving the optimal estimation problem about the clear image to obtain a clear image estimation value; solving the optimal estimation problem about the point spread function to obtain the point spread function estimation value; updating the two regularization constraint coefficients according to the obtained estimated value; and circularly executing update solution until convergence to obtain a restored image. The method can effectively solve the problems that the optimal value of the existing regularization coefficient can be obtained only by manual continuous adjustment, the efficiency is low, and the automatic operation of the program cannot be realized.
Description
Technical Field
The invention relates to the technical field of computer digital image processing, in particular to a self-adaptive fuzzy image restoration method based on regularization constraint of gradient l 0 norms and total variation.
Background
In the fields of daily photography, optical remote sensing observation, medical imaging and the like, the obtained image is often blurred due to the influence of mechanical vibration in the external environment, relative motion between an imaging object and an imaging system, atmospheric turbulence and the like, the resolving power of the obtained image is reduced, and the use value is influenced. Therefore, how to avoid the image blurring effect is important.
In general, the influence of the external factors can be counteracted by adding an auxiliary image stabilizing system to the imaging system or improving the sensitivity of the imaging device, however, the former can cause the system to become more heavy as a whole, and the latter can introduce a large amount of noise into the image, and the detail resolving power of the image is reduced. Therefore, it is important to develop a blurred image restoration method and to process a blurred image by software to improve the resolution.
Mathematically, image blurring can be described by a convolution operation of a sharp image and a point spread function, and its inverse process, i.e., a blurred image restoration process, is called deconvolution, and accurate estimation of the point spread function is a key step in achieving high quality deconvolution. The deconvolution process is a typical pathological process, i.e., noise in the blurred image with little energy is amplified and back-propagated into the restored image, causing the restored result to deviate far from a true sharp image. Therefore, an additional constraint condition, namely a regularization condition, is added to correct the problem, so that a better restoration effect is obtained. However, the regularization constraint requires the introduction of regularization coefficients whose values directly affect the accuracy of the point spread function estimation and the quality of the final restored image. The conventional method is low in efficiency and cannot realize automatic operation of the program because the optimal value of the regularization coefficient is obtained by continuously attempting to adjust by a manual method. Therefore, there is a need to design a new technical solution to comprehensively solve the problems existing in the prior art.
Disclosure of Invention
The invention aims to provide a fuzzy image restoration method based on regularization constraint of gradient l 0 norms and total variation, which can effectively solve the problems that the optimal value of the conventional regularization coefficient can be obtained only by manual continuous adjustment, the efficiency is low and automatic running of a program cannot be realized.
In order to solve the technical problems, the invention adopts the following technical scheme:
A fuzzy image restoration method based on gradient l 0 norm and total variation regularization constraint comprises the following steps:
1) Modeling fuzzy image noise by using a Gaussian probability model, modeling a clear image by using a gradient l 0 norm, and modeling a point spread function by using a total variation component to respectively obtain a fuzzy image noise model, a clear image model and a point spread function model;
2) Introducing two regularization constraint coefficients, carrying out weighted summation on a fuzzy image noise model, a clear image model and a point spread function model, and constructing a fuzzy image restoration problem model;
3) Decomposing the blurred image restoration problem model into an optimal estimation problem about a sharp image and an optimal estimation problem about a point spread function;
4) Initializing an estimated value of a clear image and initializing an estimated value of a point spread function;
5) Solving an optimal estimation problem about the clear image by using the estimation value of the fixed point diffusion function to obtain an estimation value of the clear image;
6) Fixing the estimated value of the clear image, and solving the optimal estimated problem about the point spread function to obtain the estimated value of the point spread function;
7) Updating the two regularization constraint coefficients in the step 2) according to the estimated values obtained in the steps 5) and 6);
8) And circularly executing the steps 5) to 7) until convergence, namely obtaining the estimated values of the point spread function and the clear image, and obtaining the restored image.
Step 1) is modeling under a bayesian probability framework, wherein:
modeling noise with Gaussian probability model is expressed as
Modeling an image with a gradient l 0 norm is expressed as
-ln[P(o)]∝∑isign[|(dxo)i|+|(dyo)i|]
The expression modeling the point spread function by using the total variation is
Wherein,G represents a blurred image, o represents a clear image, and h represents a point spread function; p (g|ho) is the probability of noise occurrence, P (o) is the probability of image occurrence, P (h) is the probability of point spread function occurrence, d x and d y represent horizontal and vertical gradient operators, respectively, i represents the pixel index in a clear image, and j represents the point spread function element index.
The fuzzy image restoration problem model of the step 2) is as follows:
where λ and μ are the coefficients of regularization introduced.
Step 3) the expression of the optimal estimation problem for sharp images is:
the expression for the optimal estimation problem for the point spread function is:
And 4) initializing an estimated value of the clear image by adopting the fuzzy image, and initializing an estimated value of the point spread function by adopting a two-dimensional Gaussian function.
Step 5) solving the optimal estimation problem about the clear image by adopting a secondary penalty function method, firstly introducing an auxiliary variable u, a penalty coefficient beta and a growth coefficient r, and iteratively executing the following three steps until an estimated value o of the clear image is output when beta=beta max:
51 Fixed u, solution in frequency domain
52 Fixed o, solution in spatial domain
53 Updating β, β=βr).
Step 6) solving the optimal estimation problem about the point spread function by adopting a re-weighted least square method, and iteratively executing the following two steps until an estimated value h of the point spread function is output when m=m max:
61 Using conjugate gradient method to calculate the following formula:
62 Updating m, m=m+1;
Wherein H (m) is a diagonal matrix with element values on the diagonal
Step 7) updating two regularized constraint coefficients, namely, firstly introducing an intermediate variable eta, and then executing the steps as follows:
71 Calculating an update amount:
72 Updating λ): λ=λ+d;
73 Updating the intermediate variable η): η=λ/μ+d;
74 Update μ): μ=λη.
According to the fuzzy image restoration method based on regularization constraint of the gradient l 0 norm and the total variation, provided by the technical scheme, under the Bayesian maximum posterior estimation framework, the clear image and the point diffusion function are respectively modeled by introducing the l 0 norm and the total variation of the image gradient, regularization constraint conditions are formed, and the optimal estimation problem facing the point diffusion function is comprehensively constructed. And then, an iterative optimization algorithm is adopted, so that the regularization coefficient can be continuously updated while the optimal estimated value of the point spread function is given, the manual adjustment of the regularization coefficient is avoided, the full-automatic running of the program is realized, and the high-quality point spread function and the restored image can be estimated and obtained.
The method provided by the invention can carry out synchronous self-adaptive estimation updating on the point spread function and the regularization coefficient, thereby realizing high-quality fuzzy image restoration, effectively solving the problems that the optimal value of the regularization coefficient can be obtained only by manual continuous adjustment, has lower efficiency and can not realize automatic running of the program, effectively reducing the dependence of the program on manpower, and simultaneously obtaining the restored image with high quality and high accuracy.
Drawings
FIG. 1 is a flow chart of a blurred image restoration method based on gradient l 0 norms and total variation regularization constraints of the invention;
FIG. 2 is a clear image in an embodiment of the invention;
FIG. 3 is a point spread function corresponding to a simulated image in an embodiment of the invention;
FIG. 4 is a blurred image corresponding to a sharp image in an embodiment of the present invention;
FIG. 5 is a restored image obtained according to an embodiment of the present invention;
Fig. 6 is a plot of the estimated point spread function for an embodiment of the present invention.
Detailed Description
The present invention will be specifically described with reference to examples below in order to make the objects and advantages of the present invention more apparent. It should be understood that the following text is intended to describe only one or more specific embodiments of the invention and does not limit the scope of the invention strictly as claimed.
In this embodiment, fig. 2 shows a clear image, fig. 3 shows an image of a point spread function corresponding to a blurred image, and the blurred image in fig. 4 is obtained by convolving the clear image with the point spread function and overlapping gaussian noise; in this embodiment, taking the blurred image shown in fig. 4 as an example, the technical scheme of the present invention is described, and the flowchart of the blurred image restoration method based on the regularization constraint of the gradient l 0 norm and the total variation is shown in fig. 1, and includes the following steps:
Step 1), under a Bayesian maximum posterior estimation framework, modeling noise by using a Gaussian probability model, modeling a clear image by using a gradient l 0 norm, and modeling a point spread function by using a total variation;
modeling noise with Gaussian probability model is expressed as
Modeling the image by using a gradient l 0 norm, wherein the expression is-ln [ P (o) ] - Σ isign[|(dxo)i|+|(dyo)i | ];
Modeling a point spread function by using total variation, wherein the expression is
Wherein,G represents a blurred image, o represents a clear image, and h represents a point spread function; p (g|ho) is the probability of noise occurrence, P (o) is the probability of image occurrence, P (h) is the probability of point spread function occurrence, d x and d y represent horizontal and vertical gradient operators, respectively, i represents the pixel index in a clear image, and j represents the point spread function element index.
Step 2), introducing two regularization constraint coefficients lambda and mu, carrying out weighted summation on the three models in the step 1), and constructing a fuzzy image restoration problem model, wherein the model is as follows:
Step 3), in order to optimally solve the problems, decomposing the fuzzy image restoration problem model in the step 2) into two optimal estimation problems about a clear image and a point spread function;
The expression for the optimal estimation problem for sharp images is:
the expression for the optimal estimation problem for the point spread function is:
step 4), initializing an estimated value of a clear image by using a fuzzy image, initializing an estimated value of a point spread function by using a two-dimensional Gaussian function, wherein the two-dimensional Gaussian function is a matrix of 35 x 35, the mean value is 0, the variance is 5, and the parameters of the two-dimensional Gaussian function can be adjusted according to the fuzzy degree of the image; the initialization value of each of the above variables is the starting point of the execution of the following step 5).
Step 5), solving an optimal estimation problem about the clear image by adopting a quadratic penalty function method to obtain an estimation value of the clear image;
Solving the optimal estimation problem about the clear image by adopting a secondary punishment function method, firstly introducing an auxiliary variable u, a punishment coefficient beta and a growth coefficient r, and iteratively executing the following three steps until an estimated value o of the clear image is output when beta=beta max; wherein, the initial value of β is 1, β max＝220, r=1:
51 Fixed u, solution in frequency domain
52 Fixed o, solution in spatial domain
53 Updating β, β=βr).
Step 6), fixing the estimated value of the clear image obtained in the step 5), and solving the optimal estimated problem about the point spread function by adopting a re-weighted least square method to obtain the estimated value of the point spread function;
The method for solving the optimal estimation problem of the point spread function comprises the following steps: the following two steps are iteratively performed until an estimated value h of the point spread function is output when m=m max:
61 Using conjugate gradient method to calculate the following formula:
62 Updating m, m=m+1;
Wherein H (m) is a diagonal matrix with element values on the diagonal
Step 7), updating the two regularization coefficients in the step 2) according to the estimated values obtained in the step 5) and the step 6);
specifically, an intermediate variable eta is introduced first, and then the steps are carried out as follows:
71 Calculating an update amount:
72 Updating λ): λ=λ+d;
73 Updating the intermediate variable η): η=λ/μ+d;
74 Update μ): μ=λ/η.
And 8), circularly executing the steps 5), 6) and 7) until convergence to obtain an estimated value of the clear image, wherein the obtained restored image is shown in fig. 5, and the estimated value of the point spread function is shown in fig. 6.
Comparing fig. 5 with fig. 4, it can be seen that the blurring effect of the image is effectively removed and the image details are effectively restored; comparing fig. 6 with fig. 3, it can be seen that the method of the present invention can accurately estimate the point spread function.
According to the fuzzy image restoration method based on regularization constraint of gradient l 0 norms and total variation, under the Bayesian maximum posterior estimation framework, a clear image and a point diffusion function are respectively modeled by introducing l 0 norms and total variation of image gradients, regularization constraint conditions are formed, and an optimal estimation problem facing the point diffusion function is comprehensively constructed. Then, an iterative optimization algorithm is designed, so that the regularization coefficient can be continuously updated while the optimal estimated value of the point spread function is given, the regularization coefficient is prevented from being manually adjusted, and the full-automatic operation of the program is realized; meanwhile, the invention can accurately estimate the point spread function corresponding to the blurred image, restore the blurred image with high quality, obviously improve the image quality and improve the resolution capability of image details.
While the embodiments of the present invention have been described in detail with reference to the examples, the present invention is not limited to the above embodiments, and it will be apparent to those skilled in the art that various equivalent changes and substitutions can be made therein without departing from the principles of the present invention, and such equivalent changes and substitutions should also be considered to be within the scope of the present invention.
Claims (8)
1. A fuzzy image restoration method based on gradient l 0 norm and total variation regularization constraint is characterized by comprising the following steps:
1) Modeling fuzzy image noise by using a Gaussian probability model, modeling a clear image by using a gradient l 0 norm, and modeling a point spread function by using a total variation component to respectively obtain a fuzzy image noise model, a clear image model and a point spread function model;
2) Introducing two regularization constraint coefficients, carrying out weighted summation on a fuzzy image noise model, a clear image model and a point spread function model, and constructing a fuzzy image restoration problem model;
3) Decomposing the blurred image restoration problem model into an optimal estimation problem about a sharp image and an optimal estimation problem about a point spread function;
4) Initializing an estimated value of a clear image and initializing an estimated value of a point spread function;
5) Solving an optimal estimation problem about the clear image by using the estimation value of the fixed point diffusion function to obtain an estimation value of the clear image;
6) Fixing the estimated value of the clear image, and solving the optimal estimated problem about the point spread function to obtain the estimated value of the point spread function;
7) Updating the two regularization constraint coefficients in the step 2) according to the estimated values obtained in the steps 5) and 6);
8) And circularly executing the steps 5) to 7) until convergence, namely obtaining the estimated values of the point spread function and the clear image, and obtaining the restored image.
2. The blurred image restoration method based on gradient/0 norm and total variation regularization constraint of claim 1, wherein step 1) is modeling under a bayesian maximum a posteriori estimation framework, wherein:
modeling noise with Gaussian probability model is expressed as
Modeling an image with a gradient l 0 norm is expressed as
-ln[P(o)]∝∑isign[|(dxo)i|+|(dyo)i|]
The expression modeling the point spread function by using the total variation is
Wherein,G represents a blurred image, o represents a clear image, and h represents a point spread function; p (g|ho) is the probability of noise occurrence, P (o) is the probability of image occurrence, P (h) is the probability of point spread function occurrence, d x and d y represent horizontal and vertical gradient operators, respectively, i represents the pixel index in a clear image, and j represents the point spread function element index.
3. The blurred image restoration method based on the gradient/0 norm and total variation regularization constraint of claim 2, wherein the blurred image restoration problem model of step 2) is:
where λ and μ are the coefficients of regularization introduced.
4. A blurred image restoration method based on a gradient/0 norm and total variation regularization constraint as claimed in claim 3, characterized in that the expression of step 3) for the best estimation problem of the sharp image is:
the expression for the optimal estimation problem for the point spread function is:
5. The blurred image restoration method based on the gradient/0 norm and total variation regularization constraint of claim 4, wherein: and 4) initializing an estimated value of the clear image by adopting the fuzzy image, and initializing an estimated value of the point spread function by adopting a two-dimensional Gaussian function.
6. The blurred image restoration method based on gradient l 0 norm and total variation regularization constraint of claim 5, wherein step 5) adopts a quadratic penalty function method to solve the optimal estimation problem about the sharp image, firstly introduces an auxiliary variable u, a penalty coefficient β and a growth coefficient r, and iteratively performs the following three steps until an estimated value o of the sharp image is output when β=β max:
51 Fixed u, solution in frequency domain
52 Fixed o, solution in spatial domain
53 Updating β, β=βr).
7. The blurred image restoration method based on the gradient l 0 norm and total variation regularization constraint according to claim 6, wherein step 6) adopts a re-weighted least square method to solve the optimal estimation problem about the point spread function, and the following two steps are iteratively executed until the estimated value h of the point spread function is output when m=m max:
61 Using conjugate gradient method to calculate the following formula:
62 Updating m, m=m+1;
Wherein H (m) is a diagonal matrix with element values on the diagonal
8. The method for restoring a blurred image based on regularization constraints of gradient/0 norms and total variation as set forth in claim 7, wherein the step 7) of updating two regularization constraint coefficients is performed by first introducing an intermediate variable η, and then performing the steps of:
71 Calculating an update amount:
72 Updating λ): λ=λ+d;
73 Updating the intermediate variable η): η=λ/μ+d;
74 Update μ): μ=λ/η.
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